Well yes, they drop the amount of the dividend. Plus/minus market.Depends on the stock, but i do generally. A lot of stocks will drop in price the day after ex dividend, often by a lot.
So when I say "buy the dividend" one is paying the price with the dividend. Buying ex-dividend is self explanatory and again if one wants the lower basis, by all means. Settlement day used to be 3 days, now 2, so need to watch that.